If A ⊆ B, then what is (A ∪ B) ∩ A equal to?
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Answer and explanation
Correct answer: A
Since A is a subset of B, every element of A is already contained in B. Therefore, A ∪ B = B. Intersecting this union with A gives B ∩ A = A, because all elements of A are in B. Thus (A ∪ B) ∩ A = A. Option B is the union before the final intersection, and options C and D are not generally equal to A.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
Since A is a subset of B, every element of A is already contained in B. Therefore, A ∪ B = B. Intersecting this union with A gives B ∩ A = A, because all elements of A are in B. Thus (A ∪ B) ∩ A = A. Option B is the union before the final intersection, and options C and D are not generally equal to A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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